5. A large corporation uses thousands of light bulbs every year. The brand that has been used in the past has an average life of 1000 hours with a standard deviation of 100 hours. A new brand is offered to the corporation at a price far lower than one they are paying for the old brand. It is decided that they will switch to the new brand unless it is proved with a level of significance of 5% that the new brand has smaller average life than the old brand. A random sample of 100 new brand bulbs is tested yielding an observed sample mean of 985 hours. Assuming that the standard deviation of the new brand is the same as that of the old brand, (a) What conclusion should be drawn and what decision should be made? (b) What is the probability of accepting the new brand if it has the mean life of 950 hours?
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